30 (number)
Encyclopedia
30 is the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 29
29 (number)
29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three...

 and preceding 31
31 (number)
31 is the natural number following 30 and preceding 32.- In mathematics :Thirty-one is the third Mersenne prime as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,...

.

In mathematics

30 is the sum of the first four squares, which makes it a square pyramidal number
Square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...

.



It is a primorial
Primorial
In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than multiplying successive positive integers, only successive prime numbers are multiplied...

 and is the smallest Giuga number
Giuga number
A Giuga number is a composite number n such that for each of its distinct prime factors pi we have p_i | , or equivalently such that for each of its distinct prime factors pi we have p_i^2 | ....

.

30 is the smallest sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

, and the smallest of the form where r is a prime greater than 3. 30 has an aliquot sum of 42; the second sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

 and all sphenic numbers of this form have an aliquot sum 12 greater than themselves. The aliquot sequence
Aliquot sequence
In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way:For example, the...

 of 30 is 16 members long, it comprises (30,42,54,66,78,90,144,259,45,33,15,9,4,3,1,0)

Thirty has but one number for which it is the aliquot sum: the square number
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

 841.

Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number
Semiperfect number
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number....

.

30 is the largest number such that all coprime
Coprime
In number theory, a branch of mathematics, two integers a and b are said to be coprime or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1...

s smaller than itself, except for 1, are prime
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

.

A polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...

 with thirty sides is called a tricontagon.

The icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....

 and the dodecahedron are Platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

s with 30 edges. The icosidodecahedron
Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon...

 is an Archimedean solid
Archimedean solid
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...

 with 30 vertices, and the Tutte–Coxeter graph is a symmetric graph
Symmetric graph
In the mathematical field of graph theory, a graph G is symmetric if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphismsuch that...

 with 30 vertices.

E8
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...

 has Coxeter number
Coxeter number
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group, hence also of a root system or its Weyl group. It is named after H.S.M. Coxeter.-Definitions:...

 30.

30 is a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

.

Since any group G such that |G| = pnm, where p does not divide m, has a subgroup of order pn, and 30 is the only number less than 60 that is not either a prime or of the above form, it is the only candidate for the order of a simple group
Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated...

 less than 60 that one needs other methods to reject.

Astronomy

  • Messier object
    Messier object
    The Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...

     M30
    Messier 30
    Messier 30 is a globular cluster in the Capricornus constellation. It was discovered by Charles Messier in 1764. M30 is at a distance of about 28,000 light-years away from Earth, and about 90 light-years across....

    , a magnitude 8.5 globular cluster
    Globular cluster
    A globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is...

     in the constellation
    Constellation
    In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....

     Capricornus
  • The New General Catalogue
    New General Catalogue
    The New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...

     object NGC 30
    NGC 30
    NGC 30 is a double star in Pegasus constellation. It was recorded only once by German astronomer Albert Marth on Oct 30, 1864.-External links:* on WikiSky...

    , a double star in the constellation Pegasus
    Pegasus (constellation)
    Pegasus is a constellation in the northern sky, named after the winged horse Pegasus in Greek mythology. It was one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and remains one of the 88 modern constellations.-Stars:...

  • The Saros number of the solar eclipse
    Solar eclipse
    As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...

     series which began on October 2, 2069 BC and ended on March 18, 572 BC. The duration of Saros series 30 was 1496.5 years, and it contained 84 solar eclipses. Further, the Saros number of the lunar eclipse
    Lunar eclipse
    A lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...

     series which began on June 19, 1803 BC and ended on August 18, 487 BC. The duration of Saros series 30 was 1316.2 years, and it contained 74 lunar eclipses.

In other fields

Thirty is:
  • Used (as –30–
    –30–
    –30– has been traditionally used by journalists to indicate the end of a story. There are many theories about how the usage came into being,e.g...

    ) to indicate the end of a newspaper (or broadcast) story, a copy editor's typographical notation.
  • The number of days in the months April, June, September and November (and in unusual circumstances February—see February 30)
  • The total number of major and minor keys in Western tonal music, including enharmonic equivalents
  • The minimum age for United States senators
  • In years of marriage, the pearl wedding anniversary
    Wedding anniversary
    -Official recognition:In the Commonwealth realms, one can receive a message from the monarch for 60th, 65th, and 70th wedding anniversaries, and any wedding anniversary after that...

  • The duration in years of the Thirty Years' War
    Thirty Years' War
    The Thirty Years' War was fought primarily in what is now Germany, and at various points involved most countries in Europe. It was one of the most destructive conflicts in European history....

     - 1618 to 1648.
  • The code for international direct dial phone calls to Greece
    Greece
    Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

  • The house number of 30 St Mary Axe
    30 St Mary Axe
    30 St Mary Axe, the Swiss Re Building , is a skyscraper in London's main financial district, the City of London, completed in December 2003 and opened at the end of May 2004...

     (The Gherkin)
  • The designation of Interstate 30
    Interstate 30
    Interstate 30 is an Interstate Highway in the southern United States. I-30 runs from Interstate 20 west of Fort Worth, Texas, northeast via Dallas, Texas, and Texarkana, Texas, to Interstate 40 in North Little Rock, Arkansas. The route parallels U.S. Route 67 except for the portion west of...

    , a freeway that runs from Texas
    Texas
    Texas is the second largest U.S. state by both area and population, and the largest state by area in the contiguous United States.The name, based on the Caddo word "Tejas" meaning "friends" or "allies", was applied by the Spanish to the Caddo themselves and to the region of their settlement in...

     to Arkansas
    Arkansas
    Arkansas is a state located in the southern region of the United States. Its name is an Algonquian name of the Quapaw Indians. Arkansas shares borders with six states , and its eastern border is largely defined by the Mississippi River...

  • The designation of U.S. Route 30
    U.S. Route 30
    U.S. Route 30 is an east–west main route of the system of United States Numbered Highways, with the highway traveling across the northern tier of the country. It is the third longest U.S. route, after U.S. Route 20 and U.S. Route 6. The western end of the highway is at Astoria, Oregon; the...

    , a highway that runs from Oregon
    Oregon
    Oregon is a state in the Pacific Northwest region of the United States. It is located on the Pacific coast, with Washington to the north, California to the south, Nevada on the southeast and Idaho to the east. The Columbia and Snake rivers delineate much of Oregon's northern and eastern...

     to New Jersey
    New Jersey
    New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...

  • Various other routes have been numbered "30"; for example, New York State Route 30
    New York State Route 30
    New York State Route 30 is a state highway in the central part of New York in the United States. It extends for from an interchange with NY 17 in the Southern Tier to the Canadian border in the state's North Country, where it continues into Quebec as Route 138. On a regional level,...

     which runs from the Pennsylvania border to the Canadian border
  • The designation of E30
    European route E30
    European route E 30 is an A-Class West-East European route, extending from the southern Irish port of Cork in the west to the Russian city of Omsk in the east...

    , the European route from Cork
    Cork (city)
    Cork is the second largest city in the Republic of Ireland and the island of Ireland's third most populous city. It is the principal city and administrative centre of County Cork and the largest city in the province of Munster. Cork has a population of 119,418, while the addition of the suburban...

     to Samara
    Samara, Russia
    Samara , is the sixth largest city in Russia. It is situated in the southeastern part of European Russia at the confluence of the Volga and Samara Rivers. Samara is the administrative center of Samara Oblast. Population: . The metropolitan area of Samara-Tolyatti-Syzran within Samara Oblast...

  • The number of tracks on The Beatles
    The Beatles
    The Beatles were an English rock band, active throughout the 1960s and one of the most commercially successful and critically acclaimed acts in the history of popular music. Formed in Liverpool, by 1962 the group consisted of John Lennon , Paul McCartney , George Harrison and Ringo Starr...

    ' eponymous album
    Album
    An album is a collection of recordings, released as a single package on gramophone record, cassette, compact disc, or via digital distribution. The word derives from the Latin word for list .Vinyl LP records have two sides, each comprising one half of the album...

    , usually known as The White Album
  • A stage in young adulthood
    Young adult (psychology)
    A young adult, according to Erik Erikson's stages of human development, is generally a person between the age of 20 - 40, whereas an adolescent is a person between the age of 13 - 19, although definitions and opinions vary. The young adult stage in human development precedes middle adulthood. A...

  • Part of the name of:
    • 30 Odd Foot of Grunts
      30 Odd Foot Of Grunts
      30 Odd Foot of Grunts and The Ordinary Fear of God are bands formed by actor Russell Crowe and friends.-Beginnings:In the '80s Russell Crowe and friend Billy Dean Cochran formed a band, "Roman Antix", which later evolved into the Australian rock band 30 Odd Foot of Grunts...

      , the band fronted by actor Russell Crowe
      Russell Crowe
      Russell Ira Crowe is a New Zealander Australian actor , film producer and musician. He came to international attention for his role as Roman General Maximus Decimus Meridius in the 2000 historical epic film Gladiator, directed by Ridley Scott, for which he won an Academy Award for Best Actor, a...

    • The movie title 13 Going on 30
      13 Going on 30
      13 Going on 30 is a 2004 American romantic comedy fantasy film starring Jennifer Garner and Mark Ruffalo. It has a similar premise to the classic short story Rip Van Winkle, in which a young person falls asleep and wakes up many years later as an older person...

      , starring Jennifer Garner
      Jennifer Garner
      Jennifer Anne Affleck , better known as Jennifer Garner, is an American actress and film producer. Garner gained recognition on television for her performance as CIA agent Sydney Bristow in the thriller drama series Alias, which aired on ABC for five seasons from 2001 to 2006...

    • The title of the Food Network
      Food Network
      Food Network is a television specialty channel that airs both one-time and recurring programs about food and cooking. Scripps Networks Interactive owns 70 percent of the network, with Tribune Company controlling the remaining 30 percent....

       show 30 Minute Meals
      30 Minute Meals
      30 Minute Meals is a Food Network show hosted by Rachael Ray. Her first of four shows on Food Network debuted in the fall of 2001. The show specializes in convenience cooking for those with little time to cook. The show is recorded live-to-tape, with Ray doing almost all preparation in real time...

    • 30 Days of Night
      30 Days of Night
      30 Days of Night is a three-issue horror comic book mini-series written by Steve Niles, illustrated by Ben Templesmith, and published by IDW Publishing in 2002. All three parties co-own the property....

      , a comic book miniseries and film
      30 Days of Night (film)
      30 Days of Night is a 2007 American horror film based on the comic book miniseries of the same name. The film is directed by David Slade and stars Josh Hartnett, Melissa George, and Danny Huston...

      .
  • Judas Iscariot
    Judas Iscariot
    Judas Iscariot was, according to the New Testament, one of the twelve disciples of Jesus. He is best known for his betrayal of Jesus to the hands of the chief priests for 30 pieces of silver.-Etymology:...

     betrayed Jesus
    Jesus
    Jesus of Nazareth , commonly referred to as Jesus Christ or simply as Jesus or Christ, is the central figure of Christianity...

     for 30 pieces of silver
    Thirty pieces of silver
    Thirty pieces of silver was the price for which Judas Iscariot betrayed Jesus, according to the Gospel of Matthew 26:15 in the Christian New Testament. Before the Last Supper, Judas went to the chief priests and agreed to hand over Jesus in exchange for 30 silver coins...

    . Matthew
    Gospel of Matthew
    The Gospel According to Matthew is one of the four canonical gospels, one of the three synoptic gospels, and the first book of the New Testament. It tells of the life, ministry, death, and resurrection of Jesus of Nazareth...

     26:15.
  • The number of the French department Gard
    Gard
    Gard is a département located in southern France in the Languedoc-Roussillon region.The department is named after the River Gard, although the formerly Occitan name of the River Gard, Gardon, has been replacing the traditional French name in recent decades, even among French speakers.- History...

  • 30 was the route number of the bus blown up by terrorists in Tavistock Square during the 7th July 2005 bombings in London

History and literature

  • At age 30 (according to most biblical scholars) Jesus
    Jesus
    Jesus of Nazareth , commonly referred to as Jesus Christ or simply as Jesus or Christ, is the central figure of Christianity...

     of Nazareth was baptized by John the Baptist, at the beginning of his public ministry of teaching and healing.
  • One of the rallying-cries of the 1960s student/youth protest movement was the slogan, 'Don't trust anyone over thirty'.
  • In 'The Myth of Sisyphus
    The Myth of Sisyphus
    The Myth of Sisyphus is a philosophical essay by Albert Camus. It comprises about 120 pages and was published originally in 1942 in French as Le Mythe de Sisyphe; the English translation by Justin O'Brien followed in 1955....

    ' the French existentialist Albert Camus
    Albert Camus
    Albert Camus was a French author, journalist, and key philosopher of the 20th century. In 1949, Camus founded the Group for International Liaisons within the Revolutionary Union Movement, which was opposed to some tendencies of the Surrealist movement of André Breton.Camus was awarded the 1957...

     comments that the age of thirty is a crucial period in the life of a man, for at that age he gains a new awareness of the meaning of time.
  • In Franz Kafka
    Franz Kafka
    Franz Kafka was a culturally influential German-language author of short stories and novels. Contemporary critics and academics, including Vladimir Nabokov, regard Kafka as one of the best writers of the 20th century...

    's novel 'The Trial' Joseph wakes up on the morning of his thirtieth birthday to find himself under arrest for an unspecified crime. After making many futile attempts to find the nature of the crime or the name of his accuser, Joseph dies on the eve of his thirty-first birthday.
  • The number of uprights that formed the Sarsen Circle at Stonehenge
    Stonehenge
    Stonehenge is a prehistoric monument located in the English county of Wiltshire, about west of Amesbury and north of Salisbury. One of the most famous sites in the world, Stonehenge is composed of a circular setting of large standing stones set within earthworks...

    , also the supposed number of holes forming the arrays of Y and Z Holes
    Y and Z Holes
    right|thumb|400px|A plan of the Y and Z Hole circuits at Stonehenge in relation to the central stone structureThe Y and Z Holes are two rings of concentric circuits of near identical pits cut around the outside of the Sarsen Circle at Stonehenge. The current view is that both circuits are...

     at Stonehenge.
  • Western Christianity's most prolific 20th century essayist, F. W. Boreham in 'Life at Thirty' ('Cliffs of Opal') mentions that in addition to Jesus commencing ministry at 30 (Luke 3:23), Joseph was 30 when he stood before Pharaoh, King of Egypt (Genesis 41:46), King David was 30 when he began to reign (2 Samuel 5:4), and the Levites were numbered from the age of 30 and upward (1 Chronicles 23:3). Also in that essay Boreham writes 'It was said of [the English poet] Keats, that "he ensphered himself in thirty perfect years and died, not young".'

Sports

  • In tennis, the number 30 represents the second point gained in a game.
  • The California Angels
    Los Angeles Angels of Anaheim
    The Los Angeles Angels of Anaheim are a professional baseball team based in Anaheim, California, United States. The Angels are a member of the Western Division of Major League Baseball's American League. The "Angels" name originates from the city in which the team started, Los Angeles...

     (now Los Angeles Angels of Anaheim) baseball team retired the number in honor of its most notable wearer, Nolan Ryan
    Nolan Ryan
    Lynn Nolan Ryan, Jr. , nicknamed "The Ryan Express", is a former Major League Baseball pitcher. He is currently principal owner, president and CEO of the Texas Rangers....

    , on June 16, 1992. (Ryan is the only major league player to have his number retired by three different teams, though the other two teams retired number 34 for him rather than 30). The San Francisco Giants
    San Francisco Giants
    The San Francisco Giants are a Major League Baseball team based in San Francisco, California, playing in the National League West Division....

     extended the same honor to Orlando Cepeda
    Orlando Cepeda
    Orlando Manuel Cepeda Pennes is a former Puerto Rican Major League Baseball first baseman.Cepeda was born to a poor family. His father, Pedro Cepeda, was a baseball player in Puerto Rico, which influenced his interest in the sport from a young age. His first contact with professional baseball was...

    . While on the Chicago White Sox
    Chicago White Sox
    The Chicago White Sox are a Major League Baseball team located in Chicago, Illinois.The White Sox play in the American League's Central Division. Since , the White Sox have played in U.S. Cellular Field, which was originally called New Comiskey Park and nicknamed The Cell by local fans...

    , Nick Swisher
    Nick Swisher
    Nicholas Thompson "Nick" Swisher is an outfielder for the New York Yankees. Swisher is a switch hitter who throws left-handed....

     wore the number 30 and was known as "The Dirty 30".
  • 30 is one of the more common numbers worn by hockey goaltenders (along with 31).
  • The number of New Jersey Devils
    New Jersey Devils
    The New Jersey Devils are a professional ice hockey team based in Newark, New Jersey, United States. They are members of the Atlantic Division of the Eastern Conference of the National Hockey League...

     goalie, Martin Brodeur
    Martin Brodeur
    Martin Pierre Brodeur is a French-Canadian ice hockey goaltender who has played his entire National Hockey League career with the New Jersey Devils. In his 19-year tenure with the Devils, he has won three Stanley Cup championships and has been in the playoffs every year but two...

  • Lewis Hamilton
    Lewis Hamilton
    Lewis Carl Davidson Hamilton, MBE is a British Formula One racing driver from England, currently racing for the McLaren team. He was the Formula One World Champion.Hamilton was born in Stevenage, Hertfordshire...

     became the 30th Formula One World Champion on November 2, 2008.

Music

  • The number of variations in Bach
    Bạch
    Bạch is a Vietnamese surname. The name is transliterated as Bai in Chinese and Baek, in Korean.Bach is the anglicized variation of the surname Bạch.-Notable people with the surname Bạch:* Bạch Liêu...

    's Goldberg Variations
    Goldberg Variations
    The Goldberg Variations, BWV 988, is a work for harpsichord by Johann Sebastian Bach, consisting of an aria and a set of 30 variations. First published in 1741, the work is considered to be one of the most important examples of variation form...

  • 30
    30 (album)
    -Musicians:*Harry Connick, Jr. – Piano, Vocals*Ben Wolfe – Bass on track #5 "If I Were a Bell"*Rev. James Moore – Organ, vocals on track #8 "There Is Always One More Time"...

    , album from 2001 by Harry Connick, Jr.
    Harry Connick, Jr.
    Joseph Harry Fowler Connick, Jr. is an American singer, big-band leader/conductor, pianist, actor, and composer. He has sold over 25 million albums worldwide. Connick is ranked among the top 60 best-selling male artists in the United States by the Recording Industry Association of America, with...

  • 30 Seconds to Mars
    30 Seconds to Mars
    30 Seconds to Mars is an American rock band from Los Angeles, formed in 1998. Since 2007, the band has consisted of actor Jared Leto , Shannon Leto and Tomo Miličević...

  • 30 Minutes
    30 Minutes
    "30 Minutes" is a single from t.A.T.u.'s debut English album, 200 km/h in the Wrong Lane. It was released in 2003, and is the third single off that CD. A Russian version of the song was released prior to this English version which gained a lot of attention in Russia...

    , a song by t.A.T.u
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